Problem 5
Determine, with proof, whether one can find points on the circumference of a circle with unit radius such that the distance between any two of them is a rational number.
Step 5 of 5: Repeat until 1975 points are chosen
Detailed analysis
Starting with two points and applying Step 4 inductively, we can choose 1975 distinct points. Step 3 makes every pairwise chord rational. Therefore the answer is yes.